The displacement of a simple harmonic oscillator is given by x(t) = A cos(ωt + φ

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Question: The displacement of a simple harmonic oscillator is given by x(t) = A cos(ωt + φ). What is the maximum displacement?

Options:

Correct Answer: A

Solution:

The maximum displacement in SHM is equal to the amplitude A.

The displacement of a simple harmonic oscillator is given by x(t) = A cos(ωt + φ). What is the maximum displacement?

The displacement of a simple harmonic oscillator is given by x(t) = A cos(ωt + φ). What is the maximum displacement?

Step 1: Understand the equation x(t) = A cos(ωt + φ).
Step 2: Identify the term 'A' in the equation. This term represents the amplitude.
Step 3: Recognize that the amplitude 'A' is the maximum value that the displacement x(t) can reach.
Step 4: Conclude that the maximum displacement in simple harmonic motion (SHM) is equal to the amplitude A.

Simple Harmonic Motion (SHM) – SHM is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the opposite direction.
Amplitude – The amplitude (A) is the maximum extent of a vibration or oscillation, measured from the position of equilibrium.
Displacement Function – The displacement function x(t) = A cos(ωt + φ) describes the position of the oscillator at any time t, where A is the amplitude, ω is the angular frequency, and φ is the phase constant.